Table 1 Overview of the definitions and interpretations of the causal mediation effects

CDE

Y_i(x, m) – Y_i(x^∗, m)

The direct effect of changing the individual’s exposure value from x to x*, while holding the mediator value constant at m.

PNDE

Y_i(x, M_i(x^∗)) − Y_i(x^∗, M_i(x^∗))

The natural direct effect of changing the individual’s exposure value from x to x*, while holding the mediator for that individual constant at the value that would naturally be observed under exposure value x*.

TNDE

Y_i(x, M_i(x)) − Y_i(x^∗, M_i(x))

The natural direct effect of changing the individual’s exposure value from x to x*, while holding the mediator for that individual constant at the value that would naturally be observed under exposure value x.

PNIE

Y_i(x^∗, M_i(x)) − Y_i(x^∗, M_i(x^∗))

The natural indirect effect of changing the individual’s mediator value from M(x*) to M(x), while holding the individual’s exposure value constant at x*.

TNIE

Y_i(x, M_i(x)) − Y_i(x, M_i(x^∗))

The natural indirect effect of changing the individual’s mediator value from M(x*) to M(x), while holding the individual’s exposure value constant at x.

TE

Y_i(x, M_i(x)) − Y_i(x^∗, M_i(x^∗))

The total effect of changing the individual’s exposure value from x to x*.